Quantum transport through molecular wires

We explore electron transport properties in molecular wires made of heterocyclic molecules (pyrrole, furan and thiophene) by using the Green's function technique. Parametric calculations are given based on the tight-binding model to describe the electron transport in these wires. It is observed that the transport properties are significantly influenced by (a) the heteroatoms in the heterocyclic molecules and (b) the molecule-to-electrodes coupling strength. Conductance ($g$) shows sharp resonance peaks associated with the molecular energy levels in the limit of weak molecular coupling, while they get broadened in the strong molecular coupling limit. These resonances get shifted with the change of the heteroatoms in these heterocyclic molecules. All the essential features of the electron transfer through these molecular wires become much more clearly visible from the study of our current-voltage ($I$-$V$) characteristics, and they provide several key informations in the study of molecular transport.Comment: 8 pages, 4 figure

Quantum Phase Transition in a Multi-Level Dot

We discuss electronic transport through a lateral quantum dot close to the singlet-triplet degeneracy in the case of a single conduction channel per lead. By applying the Numerical Renormalization Group, we obtain rigorous results for the linear conductance and the density of states. A new quantum phase transition of the Kosterlitz-Thouless type is found, with an exponentially small energy scale $T^*$ close to the degeneracy point. Below $T^*$, the conductance is strongly suppressed, corresponding to a universal dip in the density of states. This explains recent transport measurements.Comment: 4 pages, 5 eps figures, published versio

Electron Cotunneling in a Semiconductor Quantum Dot

We report transport measurements on a semiconductor quantum dot with a small number of confined electrons. In the Coulomb blockade regime, conduction is dominated by cotunneling processes. These can be either elastic or inelastic, depending on whether they leave the dot in its ground state or drive it into an excited state, respectively. We are able to discriminate between these two contributions and show that inelastic events can occur only if the applied bias exceeds the lowest excitation energy. Implications to energy-level spectroscopy are discussed.Comment: To be published in Phys. Rev. Let

Mesoscopic Coulomb Blockade in One-channel Quantum Dots

Signatures of "mesoscopic Coulomb blockade" are reported for quantum dots with one fully transmitting point-contact lead, T1 = 1, T2 << 1. Unlike Coulomb blockade (CB) in weak-tunneling devices (T1, T2 << 1), one-channel CB is a mesoscopic effect requiring quantum coherence. Several distinctive features of mesoscopic CB are observed, including a reduction in CB upon breaking time-reversal symmetry with a magnetic field, relatively large fluctuations of peak position as a function of magnetic field, and strong temperature dependence on the scale of the quantum level spacing.Comment: 12 pages, including 4 figure

Kondo Effect of Quantum Dots in the Quantum Hall Regime

Quantum dots in the quantum Hall regime can have pairs of single Slater determinant states that are degenerate in energy. We argue that these pairs of many body states may give rise to a Kondo effect which can be mapped into an ordinary Kondo effect in a fictitious magnetic field. We report on several properties of this Kondo effect using scaling and numerical renormalization group analysis. We suggest an experiment to investigate this Kondo effect.Comment: To appear in Phys. Rev. B (5 pages, 4 figures); references added; several changes in tex

Coulomb Blockade Fluctuations in Strongly Coupled Quantum Dots

Quantum fluctuations of Coulomb blockade are investigated as a function of the coupling to reservoirs in semiconductor quantum dots. We use fluctuations in the distance between peaks $\Delta N$ apart to characterize both the amplitude and correlation of peak motion. For strong coupling, peak motion is greatly enhanced at low temperature, but does not show an increase in peak-to-peak correlation. These effects can lead to anomalous temperature dependence in the Coulomb valleys, similar to behavior ascribed to Kondo physics.Comment: figures made smaller so download works. Revised, including new data. Related papers at http://www.stanford.edu/group/MarcusLab/grouppubs.htm

Nonperturbative analysis of coupled quantum dots in a phonon bath

Transport through coupled quantum dots in a phonon bath is studied using the recently developed real-time renormalization-group method. Thereby, the problem can be treated beyond perturbation theory regarding the complete interaction. A reliable solution for the stationary tunnel current is obtained for the case of moderately strong couplings of the dots to the leads and to the phonon bath. Any other parameter is arbitrary, and the complete electron-phonon interaction is taken into account. Experimental results are quantitatively reproduced by taking into account a finite extension of the wavefunctions within the dots. Its dependence on the energy difference between the dots is derived.Comment: 8 pages, 6 figure

Conduction through a quantum dot near a singlet-triplet transition

Kondo effect in the vicinity of a singlet-triplet transition in a vertical quantum dot is considered. This system is shown to map onto a special version of the two-impurity Kondo model. At any value of the control parameter, the system has a Fermi-liquid ground state. Explicit expressions for the linear conductance as a function of the control parameter and temperature $T$ are obtained. At T=0, the conductance reaches the unitary limit $\sim 4e^2/h$ at the triplet side of the transition, and decreases with the increasing distance to the transition at the singlet side. At finite temperature, the conductance exhibits a peak near the transition point

Multi-parameter scaling of the Kondo effect in quantum dots with an even number of electrons

We address a recent theoretical discrepancy concerning the Kondo effect in quantum dots with an even number of electrons where spin-singlet and -triplet states are nearly degenerate. We show that the discrepancy arises from the fact that the Kondo scaling involves many parameters, which makes the results depend on concrete microscopic models. We illustrate this by the scaling calculations of the Kondo temperature, $T_K$, as a function of the energy difference between the singlet and triplet states $\Delta$. $T_K(\Delta)$ decreases with increasing $\Delta$, showing a crossover from a power law with a universal exponent to that with a nonuniversal exponent. The crossover depends on the initial parameters of the model.Comment: 8 pages, 3 figure

Time-dependent DMRG Study on Quantum Dot under a Finite Bias Voltage

Resonant tunneling through quantum dot under a finite bias voltage at zero temperature is investigated by using the adaptive time-dependent density matrix renormalization group(TdDMRG) method. Quantum dot is modeled by the Anderson Hamiltonian with the 1-D nearest-neighbor tight-binding leads. Initially the ground state wave function is calculated with the usual DMRG method. Then the time evolution of the wave function due to the slowly changing bias voltage between the two leads is calculated by using the TdDMRG technique. Even though the system size is finite, the expectation values of current operator show steady-like behavior for a finite time interval, in which the system is expected to resemble the real nonequilibrium steady state of the infinitely long system. We show that from the time intervals one can obtain quantitatively correct results for differential conductance in a wide range of bias voltage. Finally we observe an anomalous behavior in the expectation value of the double occupation operator at the dot $$ as a function of bias voltage